Please give step by step solution to the above problems. 3.1: (20 points) Upon B
ID: 3859002 • Letter: P
Question
Please give step by step solution to the above problems.
3.1: (20 points) Upon Bob's request, Alice computes the encyption of a one-block message m witha randomly-generated key k using the CBC mode of AES (denoted as the PRP F), and sends him the concate nation of the IV and the CBC encryption of m under the key k, denoted as c. (The answer to the question nation of the IV a V is generated. It can does not rely on the way the IV is generated. It can be either nonce-based or randomly-generated. Also, recall that the IV is one block long.) Upon Bob's request, Alice then computes the tag t for the message nmExplanation / Answer
Answer:
3.1 In CBC (Cipher Block Chaining) mode, at a given step of process, a plain text block first undergoes an XOR operation with the cipher text block of previous step before being encrypted. At first step, an Initalization Vector (IV) is used for XOR operation with plain text block. In this way, encryption of one plain text block depends on the encryption of plain text block of previous step. Once encryption is done, IV is concatenated with cipher text blocks and sent to the other party. It is to be noted that any change in even one bit of cipher text or IV affects all cipher text blocks encrypted next.
In CBC-MAC, a message authentication code is generated using block cipher. Security of CBC-MAC depends on the security of block cipher. If block cipher is secure, the CBC-MAC is secure for fixed length messages.
In the given case, Alice uses the same key for encryption and MAC computations both. This is one of the most common mistakes made while using this technique and is susceptible for an attack.
When Alice sends a series of cipher texts C1, C2, C3... to Bob, if he is aware of al least 2 correct message-tag pairs, then he can create a new third message having any of the same tags. This message will not be part of mesages actually sent by Alice to BOB. Suppose Bob has already received a message m1 with tag t1. This message can be decrypted by using shared private key k. Now he requests a tag t2 for another message m2 from Alice. Alice sends this tag to Bob. Now Bob is having access to two correct message-tag pairs. This message can also be decrypted by using the key k. But if Bob performs XOR of first block of m2 with t1 and then concatenates the result of XOR operation with m1, it will generate a new message m3 with already existing tag t2. In this way, he will have a message not originally sent by Alice.